Profit Maximization (MR = MC)

Business Calculus · Axiom Academy

LESSON Profit Maximization (MR = MC) The golden rule for optimal business decisions The Profit Maximization Condition The most important rule in business economics: Marginal Revenue = Marginal Cost Since Marginal Profit = MR - MC, profit is maximized when: This happens exactly when MR = MC. At any production level, compare MR and MC to decide what to do: Each extra unit adds more revenue than cost. Keep making more! You've found the profit-maximizing quantity. Stop here! Each extra unit costs more than it brings in. Cut back! Don't ask "What's our total profit?" Ask "Does producing ONE MORE unit add to profit?" That's marginal thinking - and it leads to optimal decisions. Green shaded area: MR > MC, each unit adds profit Red shaded area: MR < MC, each unit subtracts from profit Intersection point: Optimal quantity x* A company produces bicycles with: Cost: C(x) = 10000 + 80x + 0.1x^2 Find the profit-maximizing quantity and price. Price: p = 200 - 0.2(200) = 160 per bike Revenue: R = 200 × 160 = 32,000 Cost: C = 10,000 + 16,000 + 4,000 = 30,000 A company finds that at their current production of 500 units, MR = 25 and MC = 30. What should they do? If MR = 50 - 0.2x and MC = 10 + 0.1x, what is the profit-maximizing quantity? You've mastered the profit maximization condition! The key to optimal business decisions

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